I don't know if my problem is a hardware or a software issue! The computer is freezing on the start-up page right before all the icons show up on the desk-top. When I use ctrl-alt-del, it tells me that Windows Explorer is not responding. I've tried to re-boot several times now. It is an older pc running Windows 98--is it dying on me?

You will have to re-install win98.Some files may have been deleted.Try re-installing it again.
The other thing that might be that your hard disk may have bad sectors in it.Hence data is unreadable from it.You can know the status of bad sectors by running scandisk.

Do you have the original win98 cd? If so go to start/run and type in sfc this will check the machine for any corrupt files. If it finds them it will ask for the cd. All you need to do is click browse and select the cd drive. The file checker will locate the ones it needs.
I'd try this before anything else.

To add a note to the SFC element, have a look at the SFC Cautions posted here. If you're not careful, things can end up worse.

Thanks for all your advice! I'll have a go with the reinstall this weekend...